Journal Comment Pyrometallurgy modelling ‘It is unworthy of excellent men to lose hours like slaves in the labour of calculation which could safely be relegated to anyone else if machines were used.’ Gottfried Wilhelm Leibniz (1646 - 1716) ‘The computer is incredibly fast, accurate, and stupid. Man is unbelievably slow, inaccurate, and brilliant. The marriage of the two is a force beyond calculation.’ Leo Cherne (1912-1999) yrometallurgical operations are essentially daring prediction was made in the March 1949 issue of concerned with the high-temperature processing Popular Mechanics: ‘Where a calculator on the ENIAC is P equipped with 18,000 vacuum tubes and weighs 30 of materials. These chemical processes can be extremely complex, involving reactions between gas, tons, computers in the future may have only 1,000 solids, liquid slag, and liquid metal (and sometimes vacuum tubes and perhaps weigh 1½ tons.’ other phases as well). In addition to the chemistry, In my own lifetime, I progressed from using log consideration must also be given to the energy supply, tables, then a slide rule, to an early scientific calculator containment, and flow of the various streams. in high school. At university, I started programming in Pyrometallurgical processes must be evaluated at many Fortran on a mainframe computer that used punched stages during their development and design, and when cards (until the late 1970s). I then used a operating changes are introduced. Because programmable calculator with less than one kilobyte of experimental work in pyrometallurgy is expensive, a memory to design heat exchangers (an oddly named system should be characterized as thoroughly as piece of equipment: even if there was a caloric-like possible before experimental work is undertaken. substance called ‘heat’, it certainly isn't exchanged) Computer simulation allows the requirements of a and cyclones. When I started work, early chemical particular process to be determined quickly and equilibrium calculations were carried out (slowly and reliably. expensively) via a Saponet satellite link to the F*A*C*T Pyrometallurgy is at least 6000 years old, with the thermodynamic database (the predecessor of FactSage) oldest known smelters being used for the production of hosted on a mainframe computer at McGill University copper in the Middle East. Mathematical modelling, at in Montreal. At that time, calculations were limited in least in its simplest form, is much older than this. The the number of elements that could be accommodated, oldest known mathematical artefact is considered to be so the time was ripe for a desktop computer program the Lebombo bone – a 35 000-year-old baboon fibula that could be applied to more complex systems. discovered in a cave in the Lebombo Mountains in Pyrosim computer software for the steady-state Swaziland in the 1970s – that has a series of 29 sequential-modular simulation of pyrometallurgical notches that were deliberately cut to help to calculate processes was initially developed at Mintek in 1985 on numbers and perhaps also measure the passage of a 64 kB Apple II computer (1 MHz), and was presented time. The abacus dates from as early as 2400 BC in at the APCOM 87 conference in 1987. Pyrosim moved Babylon, and was also found in China, Egypt, Greece, to an MS-DOS version in 1988 when it was first used and Rome, and used by the Aztecs. in industry. This software was originally developed to The earliest recognisable computers were the Mark simulate various process routes for the production of I (1944) and Mark II (1945) developed at Harvard raw stainless steel, but the structure was kept general University. These electromagnetic computers are seen enough to allow it to be used to calculate predictive as the first universal calculators (even though they steady-state mass and energy balances for a very wide lacked branching) and operated at three calculations range of processes. Pyrosim thermodynamic modelling per second. The first electronic general-purpose software was eventually installed at 95 sites in 22 computer, ENIAC (Electronic Numerical Integrator And countries on 6 continents. Computer) was built in 1946 at the University of Desktop computing improved rapidly, with a Pennsylvania. ENIAC could do simple addition or roughly 1500-fold increase in speed and storage subtraction of two ten-digit numbers at the rate of capacity, from the Apple II to a fast Pentium processor. 5000 per second, or could do 357 multiplications per A typical Pyrosim simulation would have taken over an second. ENIAC weighed 27 tons, measured 2.4 m × 0.9 hour on an Apple II, but just over three seconds on a m × 30 m, and consumed 150 kW of power. A rather 33 MHz i486 computer (1200 times faster). A study of ▲ iv MAY 2015 The Journal of The Southern African Institute of Mining and Metallurgy Journal Comment (continued) practical desktop supercomputing was carried out in temperatures, but jets of air at sonic velocity have been 1993, using a real-world benchmark, written in ‘C’, to used in converting of PGM matte; and comparisons of solve a finite-volume energy-transfer problem in two- modelling and industrial trials have been made. Fluid dimensional cylindrical geometry, using the flow analysis has become more widespread and has TriDiagonal Matrix Algorithm. The chosen reference been used to model the flow in tundishes and computer was a 50 MHz i486 computer (nominally converters. A multi-physics approach, involving the rated at 30 MIPS, or 30 million instructions per interaction between concentration fields and a second). At that time, the Pentium processor (rated at magneto-hydrodynamic description of an electric arc 100 MIPS) was not yet commercially available. Using has been used to study the effect of dust particles in a this practical test, it was found that the i486-50 was 80 furnace. Modelling of gas-solid reacting systems has times faster than the original IBM PC (4.77 MHz with been used to study the sintering of iron ore, as well as 8087 coprocessor), and the well-established Cray 2 rotary kilns for direct reduction. supercomputer was in turn 5.25 times as fast as the Pyrometallurgy superficially appears primitive and i486-50. This indicated that the Cray was only about little changed from hundreds of years ago, but is one of twice as fast as a Pentium for this type of problem. The the most challenging areas to understand and model. Cray 2 was rated at 1600 MFlop/s (million floating- The simultaneous effects of very high temperatures, point operations per second). Since that time, the energy transfer, fluid dynamics, electromagnetics, computing speed of the world's fastest supercomputer phase changes, multiphase flow, free surface flow, has increased exponentially, from about 124 GFlop/s particulate materials, and thermochemistry will provide (124 × 109) in 1994 to about 34 PFlop/s (34 × 1015) much to interest pyrometallurgical modellers of the in 2014. A typical personal computer in 2014 was able future. The dramatic increases in computing power to run at about 500 GFlop/s – much faster than the make it possible to carry out different modelling world's fastest supercomputer from 1994. approaches that earlier generations could only have If we assume that computer power will continue to dreamed about. increase in the way it has done for the past twenty years, it is interesting to consider what might become possible in years to come. For example, a fully resolved model of an industrial-scale electric arc (say 50 kA over about 0.5 m) is expected to require over 200 PFlop/s (about half a million times that of the computing power of today's personal computers). At current growth predictions, this should be achieved on the world’s fastest computer in 2017, on the 500th fastest computer in 2024, and on the desktop in 2037. R.T. Jones This edition of the Journal contains a selection of papers from the SAIMM Pyrometallurgical Modelling conference. These papers should provide a good sample of the current activities in this very dynamic field. One of the challenges encountered in modelling pyrometallurgical processes is the chemical complexity of some of the feed materials and products. How best to represent coal has challenged modellers for years, but a systematic approach to this has now been adopted. Thermodynamic modelling has been applied to chemical reaction systems using diverse feed materials and reductants to produce a wide variety of metals, from platinum to clean steel. Techno-economic models bring in the economic aspects too. The extreme conditions in pyrometallurgical reactors have also proved challenging, involving not only very high The Journal of The Southern African Institute of Mining and Metallurgy MAY 2015 v ▲.